...ly enumerable degree a, and any Turing degree s, if l ′ = 0 ′ , l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: (1) l < x < a, and =-=(2)-=- x ′ = s. 1 Introduction The topic of inverting the Turing Jump in the Turing degrees started in the 1950’s. Following the pioneering work of Kleene and Post (1954), Friedberg (1957) provided a comple...

...ree l, any computably enumerable degree a, and any Turing degree s, if l ′ = 0 ′ , l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: =-=(1)-=- l < x < a, and (2) x ′ = s. 1 Introduction The topic of inverting the Turing Jump in the Turing degrees started in the 1950’s. Following the pioneering work of Kleene and Post (1954), Friedberg (1957...